1The simplest argument for this is
that lower punishments are more likely to be payable as fines, which
are simply transfers, rather than requiring costly punishments such
as imprisonment or execution. This point is discussed at much greater
length in Friedman, D. "Reflections on Optimal Punishment or Should
the Rich Pay Higher Fines?," Research in Law and Economics,
1981.

2It will also depend on other
characteristics of the two groups that effect how likely they are to
commit the crime for a given level of expected punishment.

3If we made our model more
complicated by allowing for the fact that different methods have
different costs (making a voodoo doll might be cheaper than buying
poison), the detailed quantitative conclusions would change. The
division between those who chose the two methods would no longer be
at p=.5; some people might use the method they thought less likely to
work because it was cheaper. The logic of the argument, and the
qualitative results, would remain the same.